Others believe a currency war is already underway, and that Europe is wise for sitting it out.

"We have been in a currency war since 2010," said James Rickards, senior managing director at Tangent Capital Partners and author of Currency Wars: The Making of the Next Global Crisis. "Right now, we are in a period where the fighting is more visible."

The Fed's goal is not just to double U.S. exports, as President Obama has said, but to "import inflation" by increasing import prices, he said. This strategy is politically expedient, but it will not lead to sustained economic growth, according to Rickards.

"Europe is doing everything right," he said. "You don't promote exports with a cheap currency, you promote exports with good products."

Tom Cooley, economics professor at the NYU Stern School of Business, said the latest monetary policy moves do not constitute a currency war, although he acknowledged that there can be unintended consequences for exchange rates.

"This is a period in which economies are focused on their own recoveries," he said. "If there are spillover effects, it's not a war, it's more collateral damage."